The absolute temperature of air in a region linearly increases from T₁ to T₂ in a space of width d. Find the time taken by a sound wave to go through the region in terms of T₁, T₂, d and the speed u of sound at 273 K. Evaluate this time for T₁ = 280 K, T² = 310 K, d =33m and u = 330 m s^-1.

Question

Philoid · Accepted Answer

Given:
The absolute temperature of air in a region increases linearly from to in a space of width .

The speed of sound at 273 K is .

is the velocity of the sound at temperature .

Let us find the temperature variation at a distance in the region.

Temperature variation is given by:

⇒

⇒--------------- (i)

Evaluating this time:
Initial temperature = 280 K
Final temperature = 310 K
Space width d = 33 m

On substituting the respective values in the above equation, we get:

The absolute temperature of air in a region linearly increases from T1 to T2 in a space of width d. Find the time taken by a sound wave to go through the region in terms of T1, T2, d and the speed u of sound at 273 K. Evaluate this time for T1 = 280 K, T2 = 310 K, d =33m and u = 330 m s-1.